Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 11. Work Chapter 11. Work In this chapter we explore How many kinds of energy there are; Under what conditions energy is conserved; How a system gains or loses energy. Chapter Goal: To develop a more complete understanding of energy and its conservation.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Topics: The Basic Energy Model Work and Kinetic Energy Calculating and Using Work The Work Done by a Variable Force Force, Work, and Potential Energy Finding Force from Potential Energy Thermal Energy Conservation of Energy Power Chapter 11. Work Chapter 11. Work

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Basic Energy Model W > 0: The environment does work on the system and the system’s energy increases. W < 0: The system does work on the environment and the system’s energy decreases.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Work and Kinetic Energy Consider a force acting on a particle as the particle moves along the s-axis from s i to s f. The force component F s parallel to the s-axis causes the particle to speed up or slow down, thus transferring energy to or from the particle. We say that the force does work on the particle. The unit of work is J. As the particle is moved by this single force, its kinetic energy changes as follows:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Work and Kinetic Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Work Done by a Constant Force Consider a particle which experiences a constant force which makes an angle θ with respect to the particle’s displacement. The work done is Both F and θ are constant, so they can be taken outside the integral. Thus You should recognize this as the dot product of the force vector and the displacement vector:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.1 Pulling a suitcase QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.1 Pulling a suitcase

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Calculating the work done by a constant force

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.6 Calculating work using the dot product QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.6 Calculating work using the dot product

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.6 Calculating work using the dot product

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Work Done by a Variable Force To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following: We must evaluate the integral either geometrically, by finding the area under the cure, or by actually doing the integration.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.7 Using work to find the speed of a car QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Work-Kinetic Energy Theorem when Nonconservative Forces Are Involved A force for which the work is not independent of the path is called a nonconservative force. It is not possible to define a potential energy for a nonconservative force. If W c is the work done by all conservative forces, and W nc is the work done by all nonconservative forces, then But the work done by the conservative forces is the negative of the change in potential energy, so the work- kinetic energy theorem becomes

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.9 Using work and potential energy together QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 11.9 Using work and potential energy together

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Conservation of Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy Bar Charts We may express the conservation of energy concept as an energy equation. We may also represent this equation graphically with an energy par chart.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Power The rate at which energy is transferred or transformed is called the power, P, and it is defined as The unit of power is the watt, which is defined as 1 watt = 1 W = 1 J/s.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE Choosing a motor QUESTION: